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Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of this variable to learn about the new predicted CDF? I intend to use this CDF as one input (say sample from it) in a model that also has other random variables. If my approach isnt advisable, please recommend me an alternative.

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Try using Kernel density to estimate PDF of the distribution. If you apply Gaussian function the practical choice of bandwidth coined by Silverman is 1.06*sd(X)*n^(-1/5).

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